Image quality performance for a color marking device

ABSTRACT

What is disclosed is a novel system and method for determining printer performance in terms of image quality defects over a large complex set of conditions based on measurements taken over a small simple set of conditions, thus reducing the amount of time, effort, and wasted paper required to obtain the data. The present system and method effectively utilizes a predictive model that predicts noise measurements of multi-separations from those of single-separation colors and/or a subset of the multi-separations. Because a model is used to comprehend color performance over the entire gamut, the number of patches is reduced. This reduction enables the method to be used within a machine to dynamically characterize the device&#39;s image quality performance. Various embodiments have been disclosed.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is related to concurrently filed and co-pending U.S.patent application Ser. No. ______, entitled, “On-Paper Image QualityMetrics Using On-Belt Sensing”, (Attorney Docket No. 20090636-US-NP).

TECHNICAL FIELD

The present invention is directed to systems and methods for determiningimage quality performance of a color marking system.

BACKGROUND

With the advent of in-line sensing technologies, it has become more andmore common that color marking systems are able to gather informationabout image quality (IQ) defects and utilize that information, forexample, to improve their image quality performance. The success ofthese technologies relies heavily on the timely availability of theinformation of image quality defects. A full characterization of theentire color space for a given image quality metric, such as mottle,graininess, banding, and temporal color variations requires a largenumber of printed patches. For many applications, it can be prohibitiveto print and measure all colors of interest to build a comprehensiveimage quality performance database over a target device's entire colorgamut.

Accordingly, what is needed in this art are increasingly sophisticatedsystems and methods for determining image quality performance for anycolor of interest based upon measurements obtained for a small number ofsingle-separation colors.

BRIEF SUMMARY

What is disclosed is a novel system and method for determining printerperformance in terms of image quality (IQ) over a large complex set ofconditions based upon measurements taken over a small simple set ofconditions. The present system and method utilizes a combination ofprint noise measurements of printed separation colors, the nominalprinter model, for example, readily available from the color profiles,and statistical modeling techniques such as Monte Carlo simulation or avariance model, to predict noise of multi-separation colors from thesingle-separation colors. Because a model is used to comprehend imagequality over the entire gamut, the number of patches is reduced. In sucha manner, a given device's IQ performance can be dynamicallycharacterized within the customers print/copy job environment.Advantageously, the present method is applicable to a wide variety ofimage quality defects caused by printer noises such as, for example, 2-Drandom (non-structured) spatial noise defects, such as mottle andgraininess, 1D spatial defects, such as streaks, banding and moiré.

In one example embodiment, the present system and method for determiningimage quality variation of a color marking device involves performingthe following. First, a device-independent color variation correspondingto an image quality variation for device-dependent single-separationcolors of a target color marking device is received. A device-dependentcolor variation is estimated as a function of area-coverage for eachcolorant using said device-independent color variation which has beenselected. Also a device-independent color variation for adevice-dependent multi-separation color of interest is estimated. Thisestimation is based upon the device-dependent color variation as afunction of area-coverage. The image quality variation of the targetmarking device is determined by using the estimated device-independentcolor variation for the device-dependent multi-separation color ofinterest. The measured image quality variation may be further defined asan image quality metric. The image quality metric can be any of:graininess, mottle, banding, temporal color variation, and streaking.Each of the measured image quality metrics is converted, in a mannermore fully described herein, to a corresponding measure ofdevice-independent color variation. In various embodiments hereof, thedevice-independent color variation for a device-dependentmulti-separation color of interest is estimated using a Monte Carlosimulation. In other embodiments, the device-independent color variationfor a device-dependent multi-separation color of interest is estimatedusing a variance model. Inputs to the variance model include theestimated device-dependent color variation as a function ofarea-coverage corresponding to each colorant, and/or a Jacobian matrixof a printer model of a target marking device. The predicted imagequality variation of the target marking device can be used, for example,for performing a diagnostic, tracking, performing a maintenance,performing a color management parameter adjustment, device assessment,soft-proofing, workflow analysis, and notifying an operator.

Many features and advantages of the above-described method will becomereadily apparent from the following detailed description andaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other features and advantages of the subject matterdisclosed herein will be made apparent from the following detaileddescription taken in conjunction with the accompanying drawings, inwhich:

FIG. 1 is an example test-pattern for validating the predictive modelused to correlate on-belt to on-paper measurements for single-separationcolors;

FIG. 2 is a block diagram illustrating one example embodiment ofbuilding a prediction model for correlating on-belt measurements toon-paper measurements using the example test patter of FIG. 1 as input;

FIG. 3 is a flow diagram illustrating one example embodiment forselecting an image quality metric measured via on-belt sensing andpredicting a corresponding image quality metric on-paper;

FIG. 4 is a plot of experimental performance results for the predictionmodel of FIG. 2 as further discussed with respect to the flow diagram ofFIG. 3;

FIG. 5 is a block diagram illustrating one example embodiment fordetermining a 2-D image quality metric such as smoothness;

FIG. 6 is a block diagram of one example embodiment for determining animage quality metric such as color stability and/or color uniformity;

FIG. 7 is a block diagram of one example embodiment for determining animage quality metric such as banding;

FIG. 8 is an example engine response curve used and discussed withrespect to the example block diagrams of FIGS. 5-7;

FIG. 9 is an example colorant variation curve for NMF used and discussedwith respect to the example block diagrams of FIGS. 5-7;

FIG. 10 shows an example single-separation test-page (at 5%, 25%, 50%,60%, 75%, 100%) for Noise Mottle Frequency (NMF) from a training setthat includes only single-separation colors;

FIG. 11 shows an example testing page that includes multi-separationcolors;

FIGS. 12 and 13 are plots of the performance model discussed withrespect to the embodiments of FIGS. 10-11, using each of a Monte Carloand a Variance Model approach; and

FIG. 14 is an example functional block diagram of a color marking devicein a networked printing environment incorporating various features andembodiments of the predictive correlation model of FIGS. 2-3 and theperformance models of FIGS. 5-7.

FIG. 15 illustrates a block diagram of one example embodiment of aspecial purpose computer useful for implementing one or more aspects ofthe present method, as shown and discussed with respect to theabove-described illustrations.

DETAILED DESCRIPTION

What is disclosed is a novel system and method for determining printerperformance in terms of image quality (IQ) over a large complex set ofconditions based upon measurements taken over a small simple set ofconditions. A first system and method used to predict the correspondingIQ metric on-paper for a selected IQ metric measured on-belt from anin-line sensor. A second novel system and method is used to determine aselected IQ metric on-paper for a selected CMYK colorant of interestfrom a small sample of IQ metric measurements on-paper.

It should be understood that one of ordinary skill in this art would bereadily familiar with many facets of color science such as, but notlimited to, color space, color gamuts, gamut mapping, devicecalibration, and other related techniques and algorithms commonly foundin the digital document reproduction arts. Additionally, one of ordinaryskill would also be familiar with techniques used for color manipulationand various color transformation processes and the systems involved withcolor imaging. Those of ordinary skill would be familiar with the text:“Digital Color Imaging Handbook”, CRC Press (2003), ISBN-13:9780849309007, and “Control of Color Imaging Systems: Analysis andDesign”, CRC Press (2009), ISBN-13: 9780849337468, both of which areincorporated herein in their entirety by reference. One of ordinaryskill would also be knowledgeable about computer science and softwareand programming systems and methods sufficient to implement thefunctionality and capabilities described in detail herein in their ownhardware environments without undue experimentation.

NON-LIMITING DEFINITIONS

A “device-independent color space” is any standard color space that iscommonly used to define or describe color, e.g. CIE XYZ, CIE L*a*b*, CIEL*u*v*, sRGB etc.

A “device-dependent color space” is a color space that is non-standardand cannot be used to commonly define colors without additionalinformation such as the characteristics of the rendering device. Forexample, the commonly used CMYK color space for 4-color printers is adevice-dependent color space since the rendering of a given CMYK colorcould yield very different (device-independent) colors from one model ofa printer to another model of a printer. As another example, thenon-standard RGB space is also a device-dependent color space since therendering of an RGB image could appear differently from one model of aCRT monitor to another model of a CRT monitor.

A “color separation” refers to an individual separation corresponding toone of the colorants of a target marking system. For example, there are4 separations: C, M, Y, K for a 4-color CMYK printer. Combinations ofall color separations can be used to produce a range of colors by thetarget marking system.

A “single color separation” or “single-separation color” refers to acolor specified with only one of the color separations for a targetmarking system. For example, for a CMYK printer, a C-only test patch isa single-separation color test patch.

A “multi-separation color” refers to a color specified with more thanone of the color separations for a target marking system. For example,for a CMYK printer, a red test color is a multi-separation color testpatch, using combinations of M and Y separations at some pre-determinedlevels.

A “colorant” refers to the medium used for rendering a particular colorseparation which, in forming a multi-colored image, is combined with oneor more other colorants to achieve image colors throughout the spectrum.Each color separation thus may have its own corresponding colorant.

A “forward printer model” converts values in a device-dependent colorspace to values in a device-independent color space for a target markingsystem. An “inverse printer model” converts values in adevice-independent color space to values in a device-dependent colorspace for a target marking system. A printer model can have the form ofa look-up table (LUT) such as a 4-D LUT for a CMYK printer, or aparameterized fitted function such as a polynomial that relates inputsin device-dependent color space to outputs in device-independent colorspace. For CMYK color space as the target device-dependent color spaceand L*a*b* color space as the output device-independent color space,updating the forward printer model includes, for example, for each of aselected number of the nodes: (a) printing a patch using the specifiedCMYK components; (b) measuring the color L*a*b* of this printed patch;(c) compiling the relationship between this input CMYK specified and itscorresponding measured output L*a*b* for each node; and finally (4)storing these compiled relationships of all the nodes in the form of aLUT. This LUT can now be used to map any CMYK in device-dependent colorspace to its predicated output L*a*b* in the device-independent colorspace for a target marking system, and is thus the printer model forthis target marking system.

An “engine response curve” (ERC) gives the relationship between themeasured lightness L* or color (L*,a*,b*) developed on the paper or onan internal media, and the input contone gray level. The ERC isestimated by printing a series of strips at different input gray levelsand measuring their corresponding lightness L* or deltaE to paper toform a curve of lightness or deltaE to paper as a function of graylevel. This curve is inverted to determine the corresponding colorantchange needed in the gray level for an observed lightness variation ateach input gray level. An example engine response curve is shown anddiscussed with respect to FIG. 8.

The “process direction” is the direction of movement of a media surfaceas the media traverses the marking mechanism.

The “cross-process direction” is the direction which is orthogonal tothe process direction, i.e., perpendicular to the movement of the mediatraversing the marking mechanism.

“On-belt” refers to an imaging area within a color marking system, suchas a belt, drum, or blanket with corresponding photoreceptors andintermediates of a color marking device, prior to the final fusing ofthe image to paper.

“Color variance” is the variance of raw color data measured from animage. Typically this raw data is further processed by a mathematicaldefinition for determining a given image quality metric.

An “image quality metric” or “IQ metric” is a mathematical definitionfor determining a given image quality defect, such as, for instance,graininess (micro-uniformity), mottle (macro-uniformity), banding,streaking, and temporal color variation. The term image quality metriccan also be used to describe the underlying variation of raw color data,from which the higher-level metrics listed above are calculated. Oneexample of image quality metrics is described in International PrintQuality Standard—ISO/IEC 13660:2001. This standard specifiesdevice-independent image quality metrics, measurement methods, andanalytical procedures to describe the quality of output images fromhardcopy devices and is applicable to human-readable documents composedof binary monochrome images produced from impact printers, non-impactprinters, and copiers.

“Graininess”, as defined by ISO-13660, is the aperiodic fluctuation ofdensity at a spatial frequency greater than 0.4 cycles per millimeter inall directions. Other definitions, such as with different spatialfrequency ranges and/or measuring fluctuation at different color space(e.g. L* rather than density), exist as well. Methods to quantifygraininess are well established. One method is to print and measure atest target consisting of a gray tone scale from 0% tint (white) to 100%(black) in 10% steps. Color tone sweeps like cyan, magenta, yellow, red,green, and blue may also be included in the target. Depending on thesample being measured, it might be desirable to perform more than onegraininess measurement per patch to reduce errors introduced by samplevariability. For samples with lower perceived graininess, considermaking multiple measurements and calculating the average reflectance andaverage graininess values. In one embodiment, graininess is calculatedas follows:

${G = {^{{- 1.8}\; D} \times {\sum\limits_{f_{n}}{{V\left( f_{n} \right)} \times \sqrt{P^{\prime}\left( f_{n} \right)}}}}},$

where D is the density, V(f_(n)) is visual transfer function as functionof the mean density level and deviation from the mean, and P′(f_(n)) isthe power spectrum (compensating for aperture)

“Banding” consists of either horizontal or vertical bands, with a periodthat gradually varies from a minimum to a maximum value. Banding canthus be defined as a 1D image density variation in the processdirection. It is often periodic and it can result from errors in themechanical motion of rotating components, such as gears, pinions, androllers in the charging and development subsystems, photoreceptors andtheir drive trains, or the ROS polygon, within a marking engine. Methodsfor measuring the banding induced density variation use an imagingsystem such as an offline scanner or in-situ sensors known as EnhancedToner Area Coverage Sensors (“ETACS”). ETACS are used to measure thedensity of toner or colorant applied to or developed on aphotoconductive member. Methods for measuring banding require anaccurate profile of the density variation. Since the density variationis periodic, it can be characterized in terms of frequency (usingFourier analysis).

“Mottle” is the irregular arrangement of patches of color on an outputprint due to defective toner transfer from the belt to the image formingsurface. Mottle is similar to graininess, but on a larger spatial scale(>250 μm). Various metrics have been developed by vendors, someproprietary, which are used to determine lightness variation of mottle.ISO-13660:2001 defines mottle as the Standard Deviation (STD) of OpticalDensity (OD) (rather than L*) between 1.27×1.27 mm² and 12.7×12.7 mm²scale over a defined spatial frequency. Xerox, in one embodiment,defines mottle as the standard deviation of L* (plus an OD correction)between 1.1×1.1 mm² and 5.5×5.5 mm² scale.

“Streaking” is pseudo-random one-dimensional defects in an image thatrun parallel to the process direction. Typical defects might arise froma non-uniform LED imager, contamination of the high voltage elements ina charger, scratches in the photoreceptor surface, etc. Graininess andmottle are usually not directionally oriented whereas streaks usuallyare.

“Temporal color variation” occurs when a first color printed at time T1visually differs from the same color printed at time T2. Color variationis generally assessed by a color difference formula, ΔE (e.g. CIE DeltaE2000). The ΔE's between individual measurements and their averages is anindication of the spatial or temporal non-uniformity of the outputdevice depending on how the individual measurements were made.

Example Block Diagram for Prediction Model Construction

Reference is being made to FIG. 1 which is an example test-pattern forvalidating the predictive model used to correlate on-belt to on-papermeasurements for single-separation colors. This test pattern is of asingle color separation and is formed using techniques well known in theart from a color marking device, such as in FIG. 14. Although FIG. 1 isshown in black and white, those skilled in the art will recognize thisas a color test patch of a single separation color. In this example thesingle separation color is cyan and this is discussed further in thesection entitled “Determining A CMYK Of Interest From A Small Sample OfIQ Measurements”.

Reference is now being made to FIG. 2 which illustrates a block diagramof one example embodiment of building a prediction model for correlatingon-belt measurements to on-paper measurements using the example testpattern of FIG. 1 as input.

Data source 210, used to produce the example test pattern of FIG. 1, isan input. In this embodiment, target color patches are eithersingle-separation colors or multiple-separation colors. Target datasource 210 includes color marking device 220, calibrated on-belt sensor230, fuser 240, and calibrated on-paper sensor 250. These devices arecoupled together via data communication links 215, 225, 230, 245. Theselinks may be any type of link that permits the transmission of data,such as direct serial connections, a local area network (LAN), wide areanetwork (WAN), an intranet, the Internet, circuit wirings, and the like.The content for a print/copy job is initially provided by the customerthrough a target data source in a form acceptable to the print system.Target data source 210 may be a personal computer, a microprocessor, ascanner, a disk drive, a tape drive, a hard disk, zip drive, CD-ROMdrive, a DVD drive, a network server, a print server, a copying device,or any other known or later developed device or system that is able toprovide the image data. The target data source may include a pluralityof components including displays, user interfaces, memory, disk drives,and the like. For simplicity, it will be assumed that target data source210 comprises a personal computer although, as indicated above, thetarget data source is not limited to a personal computer.

Color marking device 220 may be any device capable of outputting a hardcopy of an image and may take the form of a laser printer, a bubble jetprinter, an ink jet printer, a copying machine, or any other known orlater developed device or system that is able to generate an image on arecording medium using the image data or data generated from the imagedata. The color marking device generates the hard copy of the imagebased on printable image data generated by the color adjustmentsubsystem. Calibrated in-line sensor 230 may be any type of device thatis capable of detecting image data from an unfused image and supplyingthe image data. The on-belt sensor is any color sensor such as afull-width array scan bar, an optical sensor, a spectrophotometer, a LEDcolor sensor and other color sensor capable of measuring spatial andtemporal image color values. Calibrated on-paper sensor 250 may be anytype of device that is capable of detecting image data from a hard copyimage and supplying the image data. For example, the calibrated on-papersensor may be any color sensor such an optical sensor, aspectrophotometer, a LED color sensor and other color sensor capable ofmeasuring spatial and temporal image color values. Both the calibratedin-line sensor 230 and the calibrated on-paper sensor 250 may be anyother known or later developed device or system that is able to measurethe color values of the image data from the hard copy image output bythe color marking device. Correlation model 260 is built or updatedusing a cross-correlation computer-implemented algorithm on the measureddata for a given IQ metric from the calibrated in-line sensor 230 andthe calibrated on-paper sensor 250. Correlation model 260 iscommunicatively connected to receive data from the calibrated in-linesensor 230 and the calibrated on-paper sensor 250 though communicationlinks 234 and 254. The image quality metrics received into thecorrelation model include L*a*b*, σ_(L*a*b*), and A_(L*a*b*)(f), whereA_(L*a*b*)(f) represents amplitude as a function of frequency.

Although for the purposes of the description hereof, the components inFIG. 2 are shown as being separate, they may be integrated into adigital copier, a computer with a built-in printer, or any otherintegrated device that is capable of producing a hard copy image output.With such a configuration, for example, the target data source 210,color marking device 230, calibrated in-line sensor 230, fuser 240,calibrated on-paper sensor 250, and correlations model 260 may becontained within a single device. Alternatively, other configurations ofFIG. 2 may be utilized without departing from the spirit and scope ofthe specification and claims herein.

Example Flow Diagram of Prediction Model Construction

Reference is now being made to FIG. 3 which is a flow diagramillustrating one example embodiment for selecting an image qualitymetric measured via on-belt sensing and predicting a corresponding imagequality metric on-paper. Flow processing begins at 302 and immediatelyproceeds to step 304.

At step 304, select an image quality metric, such as, graininess,banding, mottle, streaking, or temporal color variation. In oneembodiment, the selection is performed in response to user input 1468 orby receiving a selection over a network.

At step 306, access measurement data from the calibrated on-belt sensor220 corresponding to the selected image quality metric, e.g. L*a*b*,σ_(L*a*b*), and A_(L*a*b*)(f). This measurement data includes imagenoise on an imaging member of the selected image quality metric in asingle-separation device-dependent color for the target color markingdevice.

At step 308, use a predictive correlation model to predict thecorresponding IQ metric on-paper. This prediction uses the correlationmodel, the image noise of single-separation device-dependent colors whenprinted on a substrate. The flow diagram ends in step 310.

This novel method is used to determine image quality performance of acolor marking device. In the embodiment next described, an estimation ofimage noise performance values of multi-separation device-dependentcolors on a substrate from the projected single-separationdevice-dependent colors on a substrate is performed using a noiseprediction model. In another embodiment, the single-separation IQmeasurements can be made on-paper rather than on-belt, therebyeliminating the step of correlating between on-belt and on-papermeasurements. These on-paper measurements can be made inline or offline.These estimated noise performance values on a substrate are used then todetermine image quality performance of the target marking device. Thesingle-separation device-dependent colors in one embodiment are cyan,magenta, yellow, and black (CMYK).

In one embodiment the image noise performance values are comparedagainst any of: a manufacturer's specification, and a user-definedspecification, such as a print job. Based on this comparison, adetermination of the image noise level of the target marking devicerelative to a defined noise tolerance level. The determination caninclude performing a diagnostic on the target marking device, performingmaintenance on the target marking device, and notifying an operator ofthe target marking device. Once the current state of the target colormarketing device, is determined based on the estimate image noiseperformance values, it can be used as a basis for performing any of: acolor management parameter adjustment, device assessment, soft-proofing,and workflow analysis.

In another embodiment, the image noise performance values are collectedover time intervals. These collected values are used to project when thetarget marking device will reach a defined noise tolerance threshold,the projection being based upon any of a time, a date, a count of anumber of pages printed by the target marking device, and a number ofhours of operation of the target marking device.

Still, in another embodiment, the estimated image noise performancevalues are used to determine image quality performance of the targetmarking device. An application dependent function having at least oneuser-selected image noise attribute as an input is determined. Theuser-selected image noise attribute and the estimated image noiseperformance values are provided to the function. A spot color recipe isselected based upon an output of the function or a color profile basedupon an output of the function is derived.

Experimental Performance Results

FIG. 4 is a plot of experimental performance results for testing theprediction of the corresponding on-paper measurement for a selected IQmetric of NMF (Noise Mottle Frequency) from an in-line calibrated sensor230 on-belt. NMF is a Xerox-defined perceived-lightness measure ofmottle and is one metric used to evaluate the uniformity of a halftonearea and other areas. A lower NMF score infers a higher quality halftoneuniformity. The X-axis is the on-paper NMF measurement data and theY-axis the corresponding on-belt NMF measurement data for multiplecopies of single separation patches (such as those shown in FIG. 1) forC, M, Y, K at 10%, 20%, . . . , 100% area coverage. Notice that theresults show an acceptable result for prediction with the correlation R²of 0.91 even if a linear model is used. Prediction performance may befurther improved with a higher-order polynomial model such as aquadratic model.

It is important to note that in one embodiment, single-separation colorsare used but in another embodiment a subset of the multiple colorseparations may be used to predict the corresponding IQ metric measuredon-paper for all the multiple color separations of interest.

Embodiment for 2-D IQ Metrics, e.g., Smoothness, Mottle, Graininess

Reference is now being made to FIG. 5 which is a block diagram of anembodiment for determining 2-D IQ metrics such as smoothness. The blockdiagram is divided into two major sections. The first major section 510illustrates the first system and method to predict the corresponding IQmetric on-paper for the selected IQ metric measured on-belt from anin-line sensor. This was described previously in the section above withreference to FIGS. 2-3. The second section 520 illustrates the secondsystem and method to determine a CMYK of interest from a small sample ofIQ measurements. Beginning in block 502, data for a target color patchor patches of single color separations are sent through the colormarking system. An example of a color marking system in a printingnetwork is further described in FIG. 14 incorporating a correlationmodel of FIGS. 2-3 and an IQ metric performance model of FIGS. 5-7.Prior to the fuser in marking system 510, a calibrated on-belt sensor512 (as described in FIG. 2 as 220 and FIG. 14 as 1486) measures on-beltdata. For this example the data is in spatial L*a*b*(x,y) which is fedto an IQ metric calculation 514. In this embodiment noise mottlefrequency (NMF) is the metric selected but as described with referenceto FIGS. 6 and 7 other IQ metrics are described as well. Depending onthe print quality standard definition used for the IQ metric beingmeasured in the patch, for example high spatial frequency noise, thesensitivity a* and b* may be less important. Specifically, for the IQmetric of mottle, the values of a*, b* are not needed in many industrydefinitions of NMF. However, this is not a limitation of this invention.The method is also well suited for the definition of color mottle or 2Dcolor noises that take a* and b* into account.

In step 516 the IQ metric, in this example NMF, is correlated asdescribed above with reference to FIGS. 2-3 to yield an on-paper IQmetric for NMF from the on-belt measurements for the IQ metric for NMF.In one embodiment, if all that is desired is to predict thecorresponding IQ metric on-paper for the selected IQ metric measuredon-belt from an in-line sensor, the process in the first major section510 ends. In another embodiment, the process continues as shown bybroken line 508 to the second major section 520 illustrates the secondnovel system and method to determine a CMYK of interest from a smallsample of IQ measurements. Continuing with the second major section 520,an example for 2-D IQ metrics for determining non-structurednoises/defects such as smoothness, mottle, graininess, etc. is shown.For structured (e.g. banding, moiré) and synchronized (e.g. streaks)defects, decomposition is not required as shown in the other IQ metricsdescribed with reference to FIGS. 6-7 below.

The colors L* for mottle are obtained from the scanned test patches.These colors L* are averaged to produce the average L* value that isconverted using the following equation for optical density (OD) toobtain the average optical density for the test patches.Device-independent color variations corresponding to the IQ metric arecomputed. The noise distributions in NMF spatial frequency range aremeasured. Given a two dimensional L* pixel map of the test patches, eachpixel has a different L* value. Depending on the print quality standarddefinition being used for NMF the perceptual weights are not strippedout. In case of a NMF definition where the perceptual weights areimportant they are stripped or subtracted out in block 522 to be appliedlater in block 530. The NMF is the manipulated L* values of the scannedimage. From the mottle frequency, a standard deviation can becalculated. That standard deviation, multiplied by 100, is corrected bythe optical density (OD) as shown in EQ. 1 below. This gives us themottle value for the test patches. The perceptual weighting is basedupon a LUT of survey data which relates optical density to the HumanVisual System (HVS).

In the definition of mottle that include perceptual weights, the L*values are converted to OD using the following relationship by EQ. 1:

$\begin{matrix}{Y = \left\{ {{\begin{matrix}\left( \frac{L^{*} + 16}{116} \right)^{3} & {L^{*} \geq 7.9996} \\{L^{*}/903.3} & {otherwise}\end{matrix}{OD}} = {- {\log_{10}(Y)}}} \right.} & {{EQ}.\mspace{14mu} 1}\end{matrix}$

Again, for many standard definitions for mottle, only L* is mappedbecause *a and b* are not important in this definition.

Next the variance of the device-dependent color variations of colorσ_(L*a*b*) is converted to a device-independent colorant variance value,such as σ_(CMYK), using area-coverage of an engine response curve (ERC)524, such as that shown in FIG. 8, for the known single color separationdata for the target color patch of block 502.

The lightness variations are converted to colorant variations infunctional block 524. These colorant variations are used to constructthe NMF colorant variation curves. FIG. 9 shows an example of convertedcolorant variation curves for NMF, which is area-coverage dependent. Toselect the correct NMF colorant variation curves, the metadata 506 ofthe target color patches of single color separations is used. For IQmetrics where the contributions from a* and b* are important, two moresets of converted colorant variations for each IQ metric, i.e., one fora* and one for b*, are also constructed. These two additional convertedcolorant variations are in addition to the colorant variation curvesshown in FIG. 9. Interpolation can be performed if necessary. As anexample, let us assume that a test patch is measured at an area coverageof 50% black, and the NMF L* standard deviation (i.e. σ_(L*)) is foundto be around 5. The standard deviation 5 is the color variation atmottle frequency. The reason it is not zero is because the markingdevice or printer is not perfect. Stated differently, when the targetcolor patches of single color separations are created by the markingdevice for 50% black, every pixel is not exactly at 50%. Some pixels areabove 50% black while other pixels are below 50% black, and so on.Referring to the ERC in FIG. 8 it can be seen that L*=50±5 can be usedto determine the corresponding area coverage for the range and thusdetermine the corresponding colorant variation for NMF at 50% black.Here are more details about this conversion. To convert color (say L*)variation to colorant variation (say black, K), one can use the ERC inFIG. 9. For example, for a given variation L*=50±5, where 5 is thestandard deviation, the corresponding colorant variation in K can beestimated by (K₁-K₂)/2, where one passes L*=50−5 to the K-ERC to get K₁and L*=50±5 to the K-ERC to get K₂. By repeating this process fordifferent area-coverages of K, the colorant variation of K for NMF isdetermined as shown in FIG. 9. Similarly, by repeating the process forC, M, Y respectively, the colorant variations of C, M, Y for NMF aredetermined. The result from an experiment is shown in FIG. 9. Thiscompletes step 524; and the NMF colorant variation curves shown in FIG.9 can be used in 526. As an example, consider a color with the followingarea coverages cyan=40%, magenta=40%, yellow=0%, and black=30%. Usingthe NMF colorant variation curves in FIG. 9 the value of σ_(c) isdetermined at 40%. An examination of the cyan curve on the colorvariation plot for NMF in FIG. 9 shows that an area coverage of cyan at40% yields (by interpolation) σ_(c)≈0.4. Similarly, for an area coverageof magenta at 40%, we determine that σ_(m)≈0.4. For an area coverage ofyellow=0%, σ_(y)≈1.5. For an area coverage of black=30%, σ_(k)≈0.4.

At 526, the device-independent lightness variations are projected orestimated as device-independent color variations for any givenmulti-separation CMYK combinations of interest. This estimation of thedevice-independent color variation for a given CMYK is based upon thedevice-dependent color variations as a function of area-coverage. Anoverview of this novel projection technique is first described followedby a detailed mathematical example. The dashed box 532 in FIGS. 5, 6 and7 denotes an optional embodiment. In one optional embodiment, a varianceis imposed 532 using a Monte Carlo simulation 534 with NMF colorantvariation curves and assume noise characteristics is normaldistribution. In another optional embodiment, lightness variations forany given CMYK combination is projected via a variance model 536 withNMF colorant variation curves, the Jacobian of the nominal printer model538. In this step, it is assumed that noises or variations insingle-separations independently contribute to any CMYK combinationwhile the colorant interaction captured in printer model 538 is only inthe mean not in the variation. In another embodiment, the correlationsusing the variance model 536 approach by sparsely measuring additionaltest patches of multi-separation CMYK. However, this adds additionalmeasurement cost and is not necessary for the IQ metric of mottle. Onemain difference between the two variance approaches in 532 is how theresulting variances are assessed. In one approach, the printer model 538is used with Monte Carlo simulation 534 while alternatively the localJacobian is used with the variance model 536. When the operationalranges are close to linear locally, both yield essentially the sameresult. The variance model 536 approach has lower computational costs.But when the operational ranges are highly non-linear for instance, thecolorant variations are too large due to poor image marking device orprinter performance or the CMYK color of interest 530 happens to have avery non-linear response in that portion of the printer model, a MonteCarlo simulation 534 will yield better results and may be preferred ifthe additional computational costs are acceptable.

At 530, the image quality metric (in this example NMF) of the targetmarking device is determined by using the estimated device-independentcolor variations for the device-dependent multi-separation color ofinterest to determine image quality performance for the target markingdevice. For this example, the mottle definition uses the perceptualweight, and these are applied to the projected variance of σ_(L*a*b*)from 526. The projected or estimated NMF for the CMYK of interest 530 isgiven by combining the calculated perceptual weights (function of L*,calculated from nominal printer model 538) and the projected σ_(L*a*b*).More specifically, a model is derived for relating independent colorantvariations σ_(CMYK) to lightness variations σ_(L*a*b*) via a Jacobian ofthe printer model 538 for the target marking device or printer.

Now a detailed mathematical description of the projection technique isdescribed.

For L*, let f(•) be the functional form, which can be stored in a lookup table (LUT) that describes the printer model for lightness, i.e.L*=f(C,M,Y,K). Assume that for a given color of interest (C₀, M₀, Y₀,K₀), the colorant variations due to printer noises has the standarddeviations of (σ_(C0), σ_(M0), σ_(Y0), σ_(K0)). Assuming further thatthese colorant variations are independently distributed, then theresulting lightness (L*) variation σ_(L=L0), satisfies the following EQ.2 (component of variances):

$\begin{matrix}{\left( \sigma_{L = L_{0}} \right)^{2} = {{\left( \left. \frac{\partial f}{\partial c} \right|_{c = c_{0}} \right)^{2}\left( \sigma_{c_{0}} \right)^{2}} + {\left( \left. \frac{\partial f}{\partial m} \right|_{m = m_{0}} \right)^{2}\left( \sigma_{m_{0}} \right)^{2}} + {\left( \left. \frac{\partial f}{\partial y} \right|_{y = y_{0}} \right)^{2}\left( \sigma_{y_{0}} \right)^{2}} + {\left( \left. \frac{\partial f}{\partial k} \right|_{k = k_{0}} \right)^{2}\left( \sigma_{k_{0}} \right)^{2}}}} & {{EQ}.\mspace{14mu} 2}\end{matrix}$

That is, the color variance (σ²) of the printer model output L is alinear combination of the individual variances with the square of thelocal Jacobian slopes.

Likewise in those image quality metrics where a* and b* contributionsare desired, for a* let g(•) be the functional form, which can be storedin a look up table (LUT) that describes the printer model for a*, i.e.a*=g(C,M,Y,K). Assume that for a given color of interest (C₀, M₀, Y₀,K₀), the colorant variations due to printer noises have the standarddeviations of (σ_(C0), σ_(M0), σ_(Y0), σ_(K0)). Assuming further thatthese colorant variations are independently distributed, then theresulting a* variation σ_(a=a0), satisfies the following EQ. 3(component of variances):

$\begin{matrix}{\left( \sigma_{a = a_{0}} \right)^{2} = {{\left( \left. \frac{\partial g}{\partial c} \right|_{c = c_{0}} \right)^{2}\left( \sigma_{c_{0}} \right)^{2}} + {\left( \left. \frac{\partial g}{\partial m} \right|_{m = m_{0}} \right)^{2}\left( \sigma_{m_{0}} \right)^{2}} + {\left( \left. \frac{\partial g}{\partial y} \right|_{y = y_{0}} \right)^{2}\left( \sigma_{y_{0}} \right)^{2}} + {\left( \left. \frac{\partial g}{\partial k} \right|_{k = k_{0}} \right)^{2}\left( \sigma_{k_{0}} \right)^{2}}}} & {{EQ}.\mspace{14mu} 3}\end{matrix}$

For b*, let h(•) be the functional form, which can be stored in a lookup table (LUT) that describes the printer model for b*, i.e.b*=h(C,M,Y,K). Assume that for a given color of interest (C₀, M₀, Y₀,K₀), the colorant variations due to printer noises have the standarddeviations of (σ_(C0), σ_(M0), σ_(Y0), σ_(K0)). Assuming further thatthese colorant variations are independently distributed, then theresulting b* variation σ_(b=b0), satisfies the following EQ. 4(component of variances):

$\begin{matrix}{\left( \sigma_{b = b_{0}} \right)^{2} = {{\left( \left. \frac{\partial h}{\partial c} \right|_{c = c_{0}} \right)^{2}\left( \sigma_{c_{0}} \right)^{2}} + {\left( \left. \frac{\partial h}{\partial m} \right|_{m = m_{0}} \right)^{2}\left( \sigma_{m_{0}} \right)^{2}} + {\left( \left. \frac{\partial h}{\partial y} \right|_{y = y_{0}} \right)^{2}\left( \sigma_{y_{0}} \right)^{2}} + {\left( \left. \frac{\partial h}{\partial k} \right|_{k = k_{0}} \right)^{2}\left( \sigma_{k_{0}} \right)^{2}}}} & {{EQ}.\mspace{14mu} 4}\end{matrix}$

In the case of the variance model 536, this is extended to project orestimate variance model to include correlation i.e. remove theabove-described restriction that the colorant variations areindependently distributed.

Similar to EQ. 2, one can relieve the independence constraint by addingcorrelation terms. That is,

$\begin{matrix}{\sigma_{L}^{2} = {\quad{\begin{bmatrix}\left( \frac{\partial f}{\partial c} \right)^{2} & {\rho_{cm}\frac{\partial f}{\partial c}\frac{\partial f}{\partial m}} & {\rho_{cy}\frac{\partial f}{\partial c}\frac{\partial f}{\partial y}} & {\rho_{ck}\frac{\partial f}{\partial c}\frac{\partial f}{\partial k}} \\{\rho_{cm}\frac{\partial f}{\partial c}\frac{\partial f}{\partial m}} & \left( \frac{\partial f}{\partial m} \right)^{2} & {\rho_{my}\frac{\partial f}{\partial m}\frac{\partial f}{\partial y}} & {\rho_{mk}\frac{\partial f}{\partial m}\frac{\partial f}{\partial k}} \\{\rho_{cy}\frac{\partial f}{\partial c}\frac{\partial f}{\partial y}} & {\rho_{my}\frac{\partial f}{\partial m}\frac{\partial f}{\partial y}} & \left( \frac{\partial f}{\partial y} \right)^{2} & {\rho_{yk}\frac{\partial f}{\partial y}\frac{\partial f}{\partial k}} \\{\rho_{ck}\frac{\partial f}{\partial c}\frac{\partial f}{\partial k}} & {\rho_{mk}\frac{\partial f}{\partial m}\frac{\partial f}{\partial k}} & {\rho_{yk}\frac{\partial f}{\partial y}\frac{\partial f}{\partial k}} & \left( \frac{\partial f}{\partial k} \right)^{2}\end{bmatrix}{\quad{{{\begin{bmatrix}\sigma_{c}^{2} \\\sigma_{m}^{2} \\\sigma_{y}^{2} \\\sigma_{k}^{2}\end{bmatrix}{for}\mspace{14mu} c} = c_{0}},{m = m_{0}},{y = y_{0}},{k = {k_{0}.}}}}}}} & {{EQ}.\mspace{14mu} 5}\end{matrix}$

Note that ρ_(CM) is the correlation coefficient (from −1 to 1) betweenC&M. It is zero when the colorants are independent (thus EQ. 2 reducesto EQ. 5).

Likewise for a*,

$\begin{matrix}{\sigma_{a}^{2} = {\begin{bmatrix}\left( \frac{\partial g}{\partial c} \right)^{2} & {\rho_{cm}\frac{\partial g}{\partial c}\frac{\partial g}{\partial m}} & {\rho_{cy}\frac{\partial g}{\partial c}\frac{\partial g}{\partial y}} & {\rho_{ck}\frac{\partial g}{\partial c}\frac{\partial g}{\partial k}} \\{\rho_{cm}\frac{\partial g}{\partial c}\frac{\partial g}{\partial m}} & \left( \frac{\partial g}{\partial m} \right)^{2} & {\rho_{my}\frac{\partial g}{\partial m}\frac{\partial g}{\partial y}} & {\rho_{mk}\frac{\partial g}{\partial m}\frac{\partial g}{\partial k}} \\{\rho_{cy}\frac{\partial g}{\partial c}\frac{\partial g}{\partial y}} & {\rho_{my}\frac{\partial g}{\partial m}\frac{\partial g}{\partial y}} & \left( \frac{\partial g}{\partial y} \right)^{2} & {\rho_{yk}\frac{\partial g}{\partial y}\frac{\partial g}{\partial k}} \\{\rho_{ck}\frac{\partial g}{\partial c}\frac{\partial g}{\partial k}} & {\rho_{mk}\frac{\partial g}{\partial m}\frac{\partial g}{\partial k}} & {\rho_{yk}\frac{\partial g}{\partial y}\frac{\partial g}{\partial k}} & \left( \frac{\partial g}{\partial k} \right)^{2}\end{bmatrix}{\quad{{{\begin{bmatrix}\sigma_{c}^{2} \\\sigma_{m}^{2} \\\sigma_{y}^{2} \\\sigma_{k}^{2}\end{bmatrix}{for}\mspace{14mu} c} = c_{0}},{m = m_{0}},{y = y_{0}},{k = {k_{0}.}}}}}} & {{EQ}.\mspace{14mu} 6}\end{matrix}$

Likewise for b*,

$\begin{matrix}{\sigma_{b}^{2} = {\begin{bmatrix}\left( \frac{\partial h}{\partial c} \right)^{2} & {\rho_{cm}\frac{\partial h}{\partial c}\frac{\partial h}{\partial m}} & {\rho_{cy}\frac{\partial h}{\partial c}\frac{\partial h}{\partial y}} & {\rho_{ck}\frac{\partial h}{\partial c}\frac{\partial h}{\partial k}} \\{\rho_{cm}\frac{\partial h}{\partial c}\frac{\partial h}{\partial m}} & \left( \frac{\partial h}{\partial m} \right)^{2} & {\rho_{my}\frac{\partial h}{\partial m}\frac{\partial h}{\partial y}} & {\rho_{mk}\frac{\partial h}{\partial m}\frac{\partial h}{\partial k}} \\{\rho_{cy}\frac{\partial h}{\partial c}\frac{\partial h}{\partial y}} & {\rho_{my}\frac{\partial h}{\partial m}\frac{\partial h}{\partial y}} & \left( \frac{\partial h}{\partial y} \right)^{2} & {\rho_{yk}\frac{\partial h}{\partial y}\frac{\partial h}{\partial k}} \\{\rho_{ck}\frac{\partial h}{\partial c}\frac{\partial h}{\partial k}} & {\rho_{mk}\frac{\partial h}{\partial m}\frac{\partial h}{\partial k}} & {\rho_{yk}\frac{\partial h}{\partial y}\frac{\partial h}{\partial k}} & \left( \frac{\partial h}{\partial k} \right)^{2}\end{bmatrix}{\quad{{{\begin{bmatrix}\sigma_{c}^{2} \\\sigma_{m}^{2} \\\sigma_{y}^{2} \\\sigma_{k}^{2}\end{bmatrix}{for}\mspace{14mu} c} = c_{0}},{m = m_{0}},{y = y_{0}},{k = {k_{0}.}}}}}} & {{EQ}.\mspace{14mu} 7}\end{matrix}$

This model is more accurate and general but requires more effort sinceit requires that we characterize the correlation coefficients locallyfor all colors of interest and assume that the identified correlationcoefficients hold for a reasonable amount of time (so that constantupdates are not required). It is important to note that in this secondmajor section 520 for the 2-dimensional IQ defects such as NMF, for anygiven CMYK of interest 530 the corresponding NMF can be estimated over alarge complex set of conditions based upon measurements taken over asmall simple set of conditions for target color patches 502.

To demonstrate the feasibility hereof, experiments were done usingPrinterA and PrinterB. First, 4 single-separation test-pages (at 5%,25%, 50%, 60%, 75%, 100%) were printed (an example is shown in FIG. 10)for training the model, and ˜100 multi-separation test-pages (at 0%,25%, 50%, 75%, 100% nodes of CMYK, i.e. a total of 5⁴=625 patches) wereprinted for testing the model. An example is shown in FIG. 10. Thesepatches were then scanned and NMF measured.

The estimation model of FIG. 5 is applied using the measurement data andscans of the 4 single-separation test pages (training set) of FIG. 10. Acorresponding PrinterA or PrinterB printer model was used to predict theNMF. The result correlates well with actual NMF measurement as shown inTable 1 and illustrated in FIG. 12 (using Monte Carlo method) and FIG.13 (using Variance model method, i.e., EQ. 2).

TABLE 1 PrinterA PrinterB#1 PrinterB#2 PrinterB#3 PrinterB#4 PrinterB#5PrinterB#6 With Slope 0.9909 1.0368 1.0183 1.0276 1.0167 1.0168 1.0494Mante Carlo R² 72.99% 76.91% 78.35% 80.91% 83.48% 79.55% 80.84% WithSlope 1.0197 1.033 1.0156 1.0304 1.0433 1.0057 1.0667 Variance Model R²74.67% 77.13% 77.34% 81.33% 84.94% 79.51% 81.63%

Some of the residual errors can be accounted for by the intrinsic pageto page variations and the assumption that mottle noises are contributedindependently from each separation. Note that the good correlationindicates that the independence assumption is quite reasonable. Theperformance of the Monte Carlo approach and the variance model aresimilar. Thus, using the variance model may be preferred for manydevices.

An advantage of this method over existing methods, such as brute-forceon-paper method, is the use of in-line on-belt sensing. This enables thepossibility of constant updating of image quality databases with all thebenefits of on-belt sensing from in-line sensors. Example benefitsinclude paper-less sensing, high update rates without loss ofproductivity, and reuse of existing in-line sensors in certain markingdevices. This novel invention provides a cost-effective and feasiblesolution that is necessary for enabling various technologies.

Embodiment for Color Stability and Color Uniformity IQ Metrics

Reference is now being made to FIG. 6, which is a block diagram of anembodiment for determining IQ metrics such as color stability and/orcolor uniformity. To avoid duplication and for sake of brevity, onlythose portions of FIG. 6 which differ from block diagram FIG. 5 aredescribed. To begin in this embodiment notice the calibrated on-beltsensor 612 (as described in FIG. 2 at 220 and FIG. 14 at 1486) measureson-belt data. For this example the data is in spatial L*a*b*(x,y) ortemporal L*a*b*(t) form, which is fed to an IQ metric calculation 614.This is important especially in applications where gradual colorvariations across the page are important. One example is a “multi-up”print job where multiple identical images are formed on a single sheet,such as, a sheet of business card graphics, or identical photographs.The stripping and applying of perceptual weights in 522 and 530 are notshown in section 620 because the standard definition of the IQ metric ofcolor stability and color variations do not need these steps. Acalculation in 630 is made for the color difference formula ΔE. This isa measurement of the magnitude of difference between two colors. Oneexample of a difference formula is defined by CIE Publication 142-2001,the teachings of which are hereby incorporated by reference hereinto intheir entirety.

Likewise for FIG. 6, it is important to note that in this second majorsection 620 for the color stability or color variation IQ metric, ordevice-independent color variation can be estimated over a large complexset of conditions based upon device-dependent color measurements takenover a small simple set of conditions for target color patches 502.

Embodiment for Banding IQ Metrics

Reference is now being made to FIG. 7, which is a block diagram of anembodiment for determining IQ metrics such as banding. Again, to avoidduplication and for sake of brevity, only those portions of FIG. 7 whichdiffer from the block diagram of FIG. 5 are described.

To begin, calibrated on-belt sensor 612 (as described in FIG. 2 at 220and FIG. 14 at 1486) measures on-belt data. For this example the data isin spatial L*a*b*(x,y) which is subjected to a Fourier Analysis 714 tofind the spatial frequencies to produce A_(L*a*b*)( ω), whereA_(L*a*b*)( ω) represents amplitude as a function of frequency. Bandingis typically periodic, caused by, for example, an out-of-round drum orroller. The A_(L*a*b*)( ω) provides the spectrum of the severaldifferent frequencies of interest. Again, the stripping and applying ofperceptual weights in 522 and 528 are not shown in section 720 becausethe definition of color stability and color variations do not need thesesteps. For this example, in step 730 the image quality banding metric ofthe target marking device is determined by using the estimateddevice-independent color variations for the device-dependentmulti-separation color of interest. The image quality banding metric isused to determine image quality performance for the target markingdevice. The equations for banding will next be described.

Let f(•) be the functional form, which can be stored in a look up table(LUT) that describes the printer model for lightness, i.e.,L*=f(C,M,Y,K). Assume that for a given color of interest (C₀, M₀, Y₀,K₀), the colorant variations due to printer noises has the standarddeviations of (A_(C0), A_(M0), A_(Y0), A_(K0)). Assuming further thatthese colorant variations are independently distributed, then theresulting lightness (L*) variation σ_(L=L0), satisfies the following EQ.8 (component of variances):

$\begin{matrix}{\left( A_{L = L_{0}} \right)^{2} = {{\left( \left. \frac{\partial f}{\partial c} \right|_{c = c_{0}} \right)^{2}\left( A_{c_{0}} \right)^{2}} + {\left( \left. \frac{\partial f}{\partial m} \right|_{m = m_{0}} \right)^{2}\left( A_{m_{0}} \right)^{2}} + {\left( \left. \frac{\partial f}{\partial y} \right|_{y = y_{0}} \right)^{2}\left( A_{y_{0}} \right)^{2}} + {\left( \left. \frac{\partial f}{\partial k} \right|_{k = k_{0}} \right)^{2}\left( A_{k_{0}} \right)^{2}}}} & {{EQ}.\mspace{14mu} 8}\end{matrix}$

That is, the amplitude as a function of frequency ω (A( ω)) of theprinter model output L is the linear combination of the individualvariances with the square of the local Jacobian slopes. EQ. 8 predictsthe worst case scenario since the phase interactions among C/M/Y/K areignored and all positive terms in the right hand side of the equationare used. This can be improved by adding phase dependency to EQ. 8.Alternatively, phases can be incorporated in the Monte Carlo simulationwith various cmyk phase combinations to assess the potential range ofbanding amplitudes for the given color of interest (C₀, M₀, Y₀, K₀).

Likewise in those IQ metrics where a* and b* contributions are desired,for a* let g(•) be the functional form, which can be stored in a look uptable (LUT) that describes the printer model for a*, i.e. a*=g(C,M,Y,K).Assume that for a given color of interest (C₀, M₀, Y₀, K₀), the colorantvariations due to printer noises has the standard deviations of (σ_(C0),σ_(M0), σ_(Y0), σ_(K0)). Assuming further that these colorant variationsare independently distributed, then the resulting a* variation σ_(a=a0),satisfies the following EQ. 9 (component of variances):

$\begin{matrix}{\left( A_{a = a_{0}} \right)^{2} = {{\left( \left. \frac{\partial g}{\partial c} \right|_{c = c_{0}} \right)^{2}\left( A_{c_{0}} \right)^{2}} + {\left( \left. \frac{\partial g}{\partial m} \right|_{m = m_{0}} \right)^{2}\left( A_{m_{0}} \right)^{2}} + {\left( \left. \frac{\partial g}{\partial y} \right|_{y = y_{0}} \right)^{2}\left( A_{y_{0}} \right)^{2}} + {\left( \left. \frac{\partial g}{\partial k} \right|_{k = k_{0}} \right)^{2}\left( A_{k_{0}} \right)^{2}}}} & {{EQ}.\mspace{14mu} 9}\end{matrix}$

For b* let h(•) be the functional form, which can be stored in a look uptable (LUT) that describes the printer model for b*, i.e.,b*=h(C,M,Y,K). Assume that for a given color of interest (C₀, M₀, Y₀,K₀), the colorant variations due to printer noises has the standarddeviations of (σ_(C0), σ_(M0), σ_(Y0), σ_(K0)). Assuming further thatthese colorant variations are independently distributed, then theresulting b* variation σ_(b=b0), satisfies the following EQ. 10(component of variances):

$\begin{matrix}{\left( A_{b = b_{0}} \right)^{2} = {{\left( \left. \frac{\partial h}{\partial c} \right|_{c = c_{0}} \right)^{2}\left( A_{c_{0}} \right)^{2}} + {\left( \left. \frac{\partial h}{\partial m} \right|_{m = m_{0}} \right)^{2}\left( A_{m_{0}} \right)^{2}} + {\left( \left. \frac{\partial h}{\partial y} \right|_{y = y_{0}} \right)^{2}\left( A_{y_{0}} \right)^{2}} + {\left( \left. \frac{\partial h}{\partial k} \right|_{k = k_{0}} \right)^{2}\left( \sigma_{k_{0}} \right)^{2}}}} & {{EQ}.\mspace{14mu} 10}\end{matrix}$

In the case of the variance model 536, this is extended to project orestimate variance model to include correlation i.e. remove theabove-described restriction of that the colorant variations areindependently distributed.

A model can be formulated that is identical to Equations 5-7 above, bysubstituting the term σ with A( ω).

Likewise for FIG. 7, it is important to note that in this second majorsection 720 for banding of a given frequency, at any given CMYK ofinterest 530 the corresponding banding can be estimated over a largecomplex set of conditions based upon measurements taken over a smallsimple set of conditions for target color patches 502. In oneembodiment, the output 530, 630 and 730 of FIGS. 5-7 are used to predictimage quality performance of the target marking device. In variousembodiments, the estimated device-independent color variations can beused to predict image quality performance of the target marking device.The image quality performance can be used for performing diagnostic,tracking, performing maintenance, performing a color managementparameter adjustment, device assessment, soft-proofing, workflowanalysis, and notifying an operator. Other uses are intended to fallwithin the scope of the appended claims.

In another embodiment, nonlinearities of the image quality metric areestimated and removed from the measured image quality metrics prior toconverting each of the image quality metrics to a corresponding measureof device-independent color variation; and re-inserting the estimatednonlinearities into the measured image quality metrics prior toestimating the corresponding area-coverage dependent noise distribution.Such uses to determine image quality performance include defining anapplication dependent function having user-selected image noiseattributes as inputs and providing those attributes and the estimatedimage noise performance values to the function. A spot color recipe canbe selected based upon the output of the function. A color profile canbe derived from an output of the function.

Image noise performance values can be compared against a manufacturer'sspecification or a user-defined specification, and based upon thecomparison, the image noise level of the target marking device can bedetermined relative to a defined noise tolerance level. The image noiselevels of the target marking device can be used for performing adiagnostic and/or performing a maintenance on the target marking device,or for notifying an operator of the target marking device that the noiselevels have exceeded (or are anticipated to exceed) desired levels.

A current state of the target marking device can be determined basedupon the estimated image noise performance values and used as a basisfor performing a color management parameter adjustment, a deviceassessment, soft-proofing, and workflow analysis. Image noiseperformance values can be collected over time and stored in a historicaldatabase. Such values can be used to project when the target markingdevice will reach a defined noise tolerance threshold. These projectionscan be based upon any of: a time, a date, a count of a number of pagesprinted by the target marking device, and a number of hours of operationof the target marking device.

Schematic of Example Special Purpose Computer

Referring to FIG. 14, shown is a functional block diagram of one examplespecial purpose computer useful for implementing one or more aspects ofthe present invention including the correlation model of FIG. 2 and IQmetric performance models of FIGS. 5-7. A plurality of modules may beexecuted by either a single special purpose computer system or aplurality of special purpose computer systems in parallel. Connectionsbetween modules include both physical and logical connections. Modulesmay further include one or more software/hardware modules which mayfurther comprise an operating system, drivers, device controllers, andother apparatuses some or all of which may be connected via a network.

The special purpose computer of FIG. 14 could be implemented as aseparate computer system, an electronic circuit, or an ASIC, forexample. The nature of the implementation will depend on the processingenvironment wherein the present method finds its intended uses.

Special purpose computer system 1400 includes processor 1406 forexecuting machine executable program instructions for carrying out allor some of the present method. The processor is in communication withbus 1402. The system includes main memory 1404 for storing machinereadable instructions. Main memory may comprise random access memory(RAM) to support reprogramming and flexible data storage. Buffer 1466stores data addressable by the processor. Program memory 1464 storesmachine readable instructions for performing the present method. Adisplay interface 1408 forwards data from bus 1402 to display 1410.Secondary memory 1412 includes a hard disk 1414 and storage device 1416capable of reading/writing to removable storage unit 1418, such as afloppy disk, magnetic tape, optical disk, etc. Secondary memory 1412 mayfurther include other mechanisms for allowing programs and/or machineexecutable instructions to be loaded onto the processor. Such mechanismsmay include, for example, a storage unit 1422 adapted to exchange datathrough interface 1420 which enables the transfer of software and data.The system includes a communications interface 1424 which acts as bothan input and an output to allow data to be transferred between thesystem and external devices such as a color scanner (not shown). Exampleinterfaces include a modem, a network card such as an Ethernet card, acommunications port, a PCMCIA slot and card, etc. Software and datatransferred via the communications interface are in the form of signals.Such signal may be any of electronic, electromagnetic, optical, or otherforms of signals capable of being received by the communicationsinterface. These signals are provided to the communications interfacevia channel 1426 which carries such signals and may be implemented usingwire, cable, fiber optic, phone line, cellular link, RF, memory, orother means known in the arts.

Terms such as, computer program medium, computer readable medium,computer executable medium, and computer usable medium are used hereinto generally refer to a machine readable media such as main memory,secondary memory, removable storage device such as a hard disk, andcommunication signals. Such computer program products are means forcarrying instructions and/or data to the computer system or device. Suchcomputer program products may include non-volatile memory, such as afloppy disk, hard drive, memory, ROM, RAM, flash memory, disk memory,and other storage useful for transporting machine readable programinstructions for executing the present method. It may further include aCD-ROM, DVD, tape, cassette, or other digital or analog media, capableof having embodied thereon one or more logical programming instructionsor other machine executable codes or commands that implement andfacilitate the function, capability, and methods disclosed herein.

It should be understood that one or more aspects of the present methodare intended to be incorporated in an article of manufacture, includingone or more computer program products. The article of manufacture may beincluded on a storage device readable by a machine architecture,xerographic system, color management or other image processing system,any of which capable of executing program instructions containing thepresent method. Such an article of manufacture may be shipped, sold,leased, or otherwise provided separately either alone or as part of anadd-on, update, upgrade, download, or product suite by the assignee or alicensee hereof as part of a computer system, xerographic system,document processing system, image processing system, color managementsystem, operating system, software program, plug-in, DLL, or a storagedevice.

It will be appreciated that the above-disclosed features and functionand variations thereof may be desirably combined into many otherdifferent systems or applications. Various presently unforeseen orun-anticipated alternatives, modifications, variations, or improvementsmay become apparent and/or subsequently made by those skilled in the artwhich are also intended to be encompassed by the appended claims. Theembodiments set forth above are considered to be illustrative and notlimiting. Various changes to the above-described embodiments may be madewithout departing from the spirit and scope of the invention.

1. A computer-implemented method for determining at least one imagequality metric of a color marking device, the method comprising:receiving at least one device-independent color variation correspondingto at least one image quality metric for device-dependentsingle-separation colors of a target marking device; estimating adevice-dependent color variation as a function of area-coverage for eachcolorant using said device-independent color variation; estimating atleast one device-independent color variation for at least onedevice-dependent multi-separation color of interest, based upon saiddevice-dependent color variation as a function of area-coverage; anddetermining said image quality metric of said target marking device byusing said estimated device-independent color variation for said atleast one device-dependent multi-separation color of interest.
 2. Themethod of claim 1, wherein said image quality metric is at least one ofgraininess, mottle, banding, temporal color variation, and streaking. 3.The method of claim 1, wherein at least one device-independent colorvariation corresponding to at least one image quality metric comprisesmeasuring said device-independent color variations from at least onecolor test target printed with device-dependent single-separation colorsusing a target marking device.
 4. The method of claim 1, wherein atleast one device-independent color variation corresponding to at leastone image quality metric includes computing said device-independentcolor variation from a value of said image quality metric.
 5. The methodof claim 1, wherein estimating a device-independent color variation forat least one device-dependent multi-separation color of interestcomprises using a Monte Carlo simulation with at least one of: a printermodel of a target marking device, and said estimated device-dependentcolor variation as a function of area-coverage corresponding to eachcolorant; and a cross-colorant correlation model.
 6. The method of claim1, wherein estimating a device-independent color variation for at leastone device-dependent multi-separation color of interest comprises usinga variance model with at least one of: said estimated device-dependentcolor variation as a function of area-coverage corresponding to eachcolorant, and a Jacobian matrix of a printer model of a target markingdevice; and a cross-colorant correlation model.
 7. The method of claim1, wherein using said estimated device-independent color variationfurther comprises at least one of: performing a diagnostic, tracking,performing a maintenance, performing a color management parameteradjustment, device assessment, soft-proofing, workflow analysis, andnotifying an operator.
 8. The method of claim 3, wherein said at leastone color test target includes device-dependent multi-separation colorsin addition to said device-dependent single-separation colors.
 9. Asystem for determining at least one image quality metric of a colormarking device, said system comprising: a memory; a storage medium forstoring data; and a processor in communication with said storage mediumand said memory, said processor executing machine readable instructionsfor performing the method of: receiving at least one device-independentcolor variation corresponding to at least one image quality variationfor device-dependent single-separation colors of a target markingdevice; estimating a device-dependent color variation as a function ofarea-coverage for each colorant using said device-independent colorvariation; estimating at least one device-independent color variationfor at least one device-dependent multi-separation color of interest,based upon said device-dependent color variation as a function ofarea-coverage; and determining said image quality variation of saidtarget marking device by using said estimated device-independent colorvariation for said at least one device-dependent multi-separation colorof interest.
 10. The system of claim 9, wherein said image qualitymetric is at least one of graininess, mottle, banding, temporal colorvariation, and streaking.
 11. The system of claim 9, wherein at leastone device-independent color variation corresponding to at least oneimage quality metric comprises measuring said device-independent colorvariations from at least one color test target printed withdevice-dependent single-separation colors using a target marking device.12. The system of claim 9, wherein at least one device-independent colorvariation corresponding to at least one image quality variation includescomputing said device-independent color variation from a value of saidimage quality variation.
 13. The system of claim 9, wherein estimating adevice-independent color variation for at least one device-dependentmulti-separation color of interest comprises using a Monte Carlosimulation with at least one of: a printer model of a target markingdevice, and said estimated device-dependent color variation as afunction of area-coverage corresponding to each colorant; and across-colorant correlation model.
 14. The system of claim 9, whereinestimating a device-independent color variation for at least onedevice-dependent multi-separation color of interest comprises using avariance model with at least one of: said estimated device-dependentcolor variation as a function of area-coverage corresponding to eachcolorant, and a Jacobian matrix of a printer model of a target markingdevice; and a cross-colorant correlation model.
 15. The system of claim9, wherein using said estimated device-independent color variationfurther comprises at least one of: performing a diagnostic, tracking,performing a maintenance, performing a color management parameteradjustment, device assessment, soft-proofing, workflow analysis, andnotifying an operator.
 16. The system of claim 11, wherein said at leastone color test target includes device-dependent multi-separation colorsin addition to said device-dependent single-separation colors.
 17. Acomputer-implemented method for determining at least one image qualitymetric of a color marking device, the method comprising: reading atleast one single color test target printed with device-dependentsingle-separation colors using a target marking device; measuring fromthe single-separation color test patch at least one device-independentcolor variation corresponding to at least one image quality variationfor device-dependent single-separation colors of the target markingdevice, wherein the image quality metric is at least one of graininess,mottle, banding, temporal color variation, and streaking; estimating adevice-dependent color variation as a function of area-coverage for eachcolorant using said device-independent color variation; estimating atleast one device-independent color variation for at least onedevice-dependent multi-separation color of interest, based upon saiddevice-dependent color variation as a function of area-coverage;determining said image quality metric of said target marking device byusing said estimated device-independent color variation for said atleast one device-dependent multi-separation color of interest; andcomputing said device-independent color variation from a value of saidimage quality metric.